Any claim can be inverted, so lacking evidence in either direction, this applies to the inverse as well.
I personally prefer more psychologically rooted arguments that lean towards at least compatibilism. If a belief in free will, regardless of the actual fact, is sufficient to affect one's actions, is that not evidence against hard determinism?
Right, but lacking any physical evidence in either direction, is it not reasonable to then turn to purely rational explanations if we want to arrive at some sort of belief?
You can have a rational basis for a belief without empirical evidence (Russell's teapot, for example). The reason you'd want to do that is to simplify the model of reality you're working with in order to reduce the number of contingencies you need to account for.
Sure, but the compatibilist view is, in my understanding, that determinism is true, but we still have free will. The mind is so complex its deterministic function can't be fully predicted, so the outcome of particular inputs over any meaningful duration cannot be computed. Thus actual free will and the illusion of free are essentially functionally identical.